A porous thermoviscoelastic mixture problem: numerical analysis and computational experiments

ABSTRACT

In this paper, we study, from the numerical point of view, a porous thermoviscoelastic mixture problem. The mechanical problem is written as a linear coupled system of two hyperbolic partial differential equations for the porosities and a parabolic partial differential equation for the temperature field. An existence and uniqueness result and an energy decay property are stated. Then, fully discrete approximations are introduced by using the finite element method to approximate the spatial variable and the backward Euler scheme to discretize the time derivatives. A priori error estimates are proved from which, under suitable regularity conditions, the linear convergence of the algorithm is derived. Finally, some numerical simulations are presented to demonstrate the accuracy of the approximations in an academical one-dimensional example and the behaviour of the solutions in one- and two-dimensional problems.

KEYWORDS:

• Mixtures
• thermoviscoelasticity
• porosity
• finite element approximations
• error estimates
• numerical simulations

AMS SUBJECT CLASSIFICATIONS:

• 65M60
• 65M15
• 65M12
• 74F05
• 74K10
• 74F10

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work has been supported by the Ministerio de Economía y Competitividad under the research projects [MTM2012-36452-C02-02], [MTM2014-51485-ERC].